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Probability mass function problem

  1. Jan 24, 2013 #1
    1. The problem statement, all variables and given/known data
    1. The sample space Ω of a certain experiment are the values 1, 2, 3, 4 and
    5 and the probability assigned to a possible value w is proportional
    to w2.
    (a) What is the probability mass function p(w) for this probability
    space?
    (b) What probability does this mass function assign to the interval
    (1; 3]?


    2. Relevant equations



    3. The attempt at a solution
    The hardest part for me to understand is the probabilities being proportional to w2. I believe the probabilities for w are 1/15, 2/15, 3/15, 4/15 and 5/15, but I'm not sure. If somebody could clear this up for me it would really help. What does it mean for w to be proportional to w2?
     
  2. jcsd
  3. Jan 24, 2013 #2

    tiny-tim

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    hi mcafej! :smile:
    call them A B C D and E instead of 1 2 3 4 and 5 …

    then P(E) = 25P(A), P(D) = 16P(A), P(C) = 9P(A), P(B) = 4P(A) :wink:
     
  4. Jan 24, 2013 #3

    HallsofIvy

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    That means that P(1)= k, P(2)= 2k, P(3)= 3k, P(4)= 4k, and P(5)= 5k for some number k.

    Use the fact that the probabilities must sum to 1 to find k.

    That "interval" is really the set {2, 3} so the probability is P(2)+ P(3).

     
  5. Jan 24, 2013 #4

    Ray Vickson

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    It does NOT say that w is proportional to w^2; it says the probability of w is proportional to w^2. Just give the word "proportional" its usual meaning.
     
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